Quasiconformal Space Mappings

Author : Matti Vuorinen
Publisher : Springer
Page : 156 pages
File Size : 41,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470618

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Quasiconformal Space Mappings by Matti Vuorinen Pdf

This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These surveys cover or are related to several topics including inequalities for conformal invariants and extremal length, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear potential theory, variational calculus, value distribution theory of quasiregular maps, topological properties of discrete open mappings, the action of quasiconformal maps in special classes of domains, and global injectivity theorems. The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in 1960 and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists. CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions.- F.W. Gehring: Topics in quasiconformal mappings.- T.Iwaniec: L(p)-theory of quasiregular mappings.- O. Martio: Partial differential equations and quasiregular mappings.- Yu.G. Reshetnyak: On functional classes invariant relative to homothetics.- S. Rickman: Picard's theorem and defect relation for quasiconformal mappings.- U. Srebro: Topological properties of quasiregular mappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems.

Author : Matti Vuorinen
Publisher : Unknown
Page : 160 pages
File Size : 48,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662164205

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Quasiconformal Space Mappings by Matti Vuorinen Pdf

Author : Alexander Vasil'ev
Publisher : Springer
Page : 214 pages
File Size : 46,7 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540454373

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Moduli of Families of Curves for Conformal and Quasiconformal Mappings by Alexander Vasil'ev Pdf

The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmüller spaces.

Author : Yunping Jiang,Sudeb Mitra
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 40,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853405

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Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces by Yunping Jiang,Sudeb Mitra Pdf

This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.

Author : Saminathan Ponnusamy,T. Sugawa,Matti Vuorinen
Publisher : Unknown
Page : 378 pages
File Size : 42,5 Mb
Release : 2007
Category : Mathematics
ISBN : PSU:000061002678

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Quasiconformal Mappings and Their Applications by Saminathan Ponnusamy,T. Sugawa,Matti Vuorinen Pdf

"Quasiconformal Mappings and their Applications covers conformal invariance and conformally invariant metrics, hyperbolic-type metrics and hyperbolic geodesics, isometries of relative metrics, uniform spaces and Gromov hyperbolicity, quasiregular mappings and quasiconformal mappings in n-space, universal Teichmuller space and related topics, quasiminimizers and potential theory, and numerical conformal mapping and circle packings."--BOOK JACKET.

Author : Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206057

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Quasiconformal Mappings and Analysis by Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka Pdf

In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Author : Lars Valerian Ahlfors
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 45,6 Mb
Release : 2006-07-14
Category : Mathematics
ISBN : 9780821836446

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Lectures on Quasiconformal Mappings by Lars Valerian Ahlfors Pdf

Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Author : MAVINA KRISHNA VAMANAMURTHY
Publisher : Unknown
Page : 94 pages
File Size : 49,7 Mb
Release : 1969
Category : Electronic
ISBN : OCLC:68278235

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QUASICONFORMAL MAPPINGS IN SPACE. by MAVINA KRISHNA VAMANAMURTHY Pdf

Author : V.M. Gol'dshtein,Yu.G. Reshetnyak
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400919228

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Quasiconformal Mappings and Sobolev Spaces by V.M. Gol'dshtein,Yu.G. Reshetnyak Pdf

'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series

Author : Parisa Hariri,Riku Klén,Matti Vuorinen
Publisher : Springer Nature
Page : 504 pages
File Size : 49,7 Mb
Release : 2020-04-11
Category : Mathematics
ISBN : 9783030320683

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Conformally Invariant Metrics and Quasiconformal Mappings by Parisa Hariri,Riku Klén,Matti Vuorinen Pdf

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

Author : Vesna Todorčević
Publisher : Springer
Page : 163 pages
File Size : 45,6 Mb
Release : 2020-08-15
Category : Mathematics
ISBN : 3030225933

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Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics by Vesna Todorčević Pdf

The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.

Author : I_Uri_ Grigor_evich Reshetni_ak
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 49,8 Mb
Release : 1989-12-31
Category : Mathematics
ISBN : 0821898213

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Space Mappings with Bounded Distortion by I_Uri_ Grigor_evich Reshetni_ak Pdf

This book is intended for researchers and students concerned with questions in analysis and function theory. The author provides an exposition of the main results obtained in recent years by Soviet and other mathematicians in the theory of mappings with bounded distortion, an active direction in contemporary mathematics. The mathematical tools presented can be applied to a broad spectrum of problems that go beyond the context of the main topic of investigation. For a number of questions in the theory of partial differential equations and the theory of functions with generalized derivatives, this is the first time they have appeared in an internationally distributed monograph.

Author : Kari Astala,Tadeusz Iwaniec,Gaven Martin
Publisher : Princeton University Press
Page : 708 pages
File Size : 51,7 Mb
Release : 2009-01-18
Category : Mathematics
ISBN : 0691137773

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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by Kari Astala,Tadeusz Iwaniec,Gaven Martin Pdf

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Author : Alastair Fletcher,Vladimir Markovic
Publisher : OUP Oxford
Page : 208 pages
File Size : 51,7 Mb
Release : 2007
Category : Mathematics
ISBN : STANFORD:36105122854339

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Quasiconformal Maps and Teichmüller Theory by Alastair Fletcher,Vladimir Markovic Pdf

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Author : Petru Caraman
Publisher : CRC Press
Page : 554 pages
File Size : 45,8 Mb
Release : 1974
Category : Mathematics
ISBN : 0856260053

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N-Dimensional Quasiconformal (QCf) Mappings by Petru Caraman Pdf